Forte coolly volleyed home a perfect cross from former Wolves striker Jake Cassidy with seven minutes remaining, and it was no more than the impressive Latics deserved after playing the better football for most of the game.
Walsall thought they were heading for a win when they took the lead in the eighth minute with a smartly worked goal. Romaine Sawyers rammed home a spectacular right-foot drive from the edge of the box after good work by Tom Bradshaw.
But after that Oldham were stronger in midfield and caused many problems for home defence, with skipper Liam Kelly pulling the strings, and he hammered two shots off target as the visitors pushed forward.
Walsall went close with an Andy Taylor free-kick in the second half, and Bradshaw wasted a chance to win it in the 90th minute when he fired over the crossbar.